Synchronized neural activity, in which the firing of neurons is coordinated in time, is an observed phenomenon in many neural functions. The conditions that promote synchrony and the dynamics of synchronized activity are active areas of investigation because they are incompletely understood. In addition, variability is intrinsic to biological systems, but the effect of neuron spike time variability on synchronization dynamics is a question that merits more attention. Previous experiments using a hybrid circuit of one biological neuron coupled to one computational neuron revealed that irregularity in biological neuron spike timing could change synchronization in the circuit, transitioning the activity between phase-locked and phase slipping. Simulations of this circuit could not replicate the transitions in network activity if neuron period was represented as a Gaussian process, but could if a process with history and a stochastic component were used. The phase resetting curve (PRC), which describes how neuron cycles change in response to input, can be used to construct a map that predicts if synchronization will occur in hybrid circuits. Without modification, these maps did not always capture observed network activity. I conducted long-term recordings of invertebrate neurons and show that interspike interval (ISI) can be represented as an autoregressive integrated moving average process, where ISI is dependent on past history and a stochastic component with history. Using integrate and fire model simulations, I suggest that stochastic activity in adaptation channels could be responsible for the history dependence and correlational structure observed in these neurons. This evidence for stochastic, history-dependent noise in neural systems indicates that our understanding of network dynamics could be enhanced by including more complex, but relevant, forms of noise. I show that cycle-by-cycle dynamics of the coupled system can be used to infer features of the dynamic map, even if it cannot be measured or is changing over time. Using this method, stable fixed points can be distinguished from ghost attractors in the presence of noise, networks with similar phase but different underlying dynamics can be resolved, and the movement of stable fixed points can be observed. The time-series vector method is a valuable tool for distinguishing dynamics and describing robustness. It can be adapted for use in larger populations and non-reciprocal circuits. Finally, some larger implications of neuroscience research, specifically the use of neural interfaces for national security, are discussed. Neural interfaces for human enhancement in a national security context raise a number of unique ethical and policy concerns not common to dual use research of concern or traditional human subjects research. Guidelines about which technologies should be developed are lacking. We discuss a two-step framework with 1) an initial screen to prioritize technologies that should be reviewed immediately, and 2) a comprehensive ethical review regarding concerns for the enhanced individual, operational norms, and multi-use applications in the case of transfer to civilian contexts.

No description available.

No description available.

This thesis consists in the study of a periodically forced slow-fast system in both its excitable and oscillatory regimes. The slow-fast system under consideration is the FitzHugh-Nagumo model, and the periodic forcing consists of a train of Gaussian-shaped pulses, the width of which is much shorter than the action potential duration. This system is a qualitative model for both an excitable cell and a spontaneously beating cell submitted to periodic electrical stimulation. Such a configuration has often been studied in cardiac electrophysiology, due to the fact that it constitutes a simplified model of the situation of a cardiac cell in the intact heart, and might therefore contribute to the understanding of cardiac arrhythmias. Using continuation methods (AUTO software), we compute periodic-solution branches for the periodically forced system, taking the stimulation period as bifurcation parameter. We then study the evolution of the resulting bifurcation diagram as the stimulation amplitude is raised. In both the excitable and the oscillatory regimes, we find that a critical amplitude of stimulation exists below which the behaviour of the system is trivial: in the excitable case, the bifurcation diagram is restricted to a stable subthreshold period-1 branch, and in the oscillatory case, all the stable periodic solutions belong to isolated loops (i.e., to distinct closed solution branches). Due to the slow-fast nature of the system, the changes that take place in the bifurcation diagram as the critical amplitude is crossed are drastic, while the way the bifurcation diagram re-simplifies above some second amplitude is much more gentle. In the oscillatory case, we show that the critical amplitude is also the amplitude at which the topology of phase-resetting changes type. We explain the origin of this coincidence by considering a one-dimensional discrete map of the circle derived from the phase-resetting curve of the oscillator (the phase-resetting map), map which constitutes a good approximation of the original differential equations under certain conditions. We show that the bifurcation diagram of any such circle map, where the bifurcation parameter appears only in an additive fashion, is always characterized by the period-1 solutions belonging to isolated loops when the topological degree of the map is one, while these period-1 solutions belong to a unique branch when the topological degree of the map is zero.

Rhythmic neural activity is thought to underlie many high-level functions of the nervous system. Our goals are to understand rhythmic activity starting with small networks, using theoretical and experimental tools. Phase resetting theory describes essential properties that cause and destroy rhythms. We validate and extend one branch of this theory, testing it in bursting neurons coupled by excitation and then extending the theory to account for temporal variability found in our experimental data. We show that the theory makes good predictions of rhythmic activity in heterogeneous networks. We also note differences in mathematical structure between inhibition- and excitation-coupling that cause them to behave differently in noisy contexts and may explain why all central pattern generators (CPGs) found in nature are dominated by inhibition. Our extension of the theory gives a method that is useful to compare experimental and model data and shows that noise may either create or destroy a rhythm. Finally, we described the cellular mechanisms in Aplysia that switch the feeding CPG from arrhythmic to rhythmic behavior in response to reward stimuli. Previous studies showed that a Dopamine reward signal is correlated to changes in electrical coupling and excitability in several important neurons in the CPG. Using the dynamic clamp and an in vitro analog of the full behavioral system, we were able to determine that electrical coupling alone controls rhythmicity, while excitability independently controls the rate of activity. These results beg for further study, including new theory to explain them fully.

Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. The cellular and molecular mechanisms underlying the ability of these networks to maintain functional stability remain poorly understood. Central pattern generating circuits produce a stable, predictable rhythm, making them ideal candidates for studying mechanisms of activity maintenance. By identifying and characterizing the regulators of activity in small neuronal circuits, we not only obtain a clearer understanding of how neural activity is generated, but also arm ourselves with knowledge that may eventually be used to improve medical care for patients whose normal nervous system activity has been disrupted through trauma or disease. We utilize the pattern-generating pyloric circuit in the crustacean stomatogastric nervous system to investigate the general scientific question: How are specific aspects of rhythmic activity regulated in a small neuronal network? The first aim of this thesis poses this question in the context of a single neuron. We used a single-compartment model neuron database to investigate whether co-regulation of ionic conductances supports the maintenance of spike phase in rhythmically bursting “pacemaker” neurons. The second aim of the project extends the question to a network context. Through a combination of computational and electrophysiology studies, we investigated how the intrinsic membrane conductances of the pacemaker neuron influence its response to synaptic input within the framework of the Phase Resetting Curve (PRC). The third aim of the project further extends the question to a systems-level context. We examined how ambient temperatures affect the stability of the pyloric rhythm in the intact, behaving animal. The results of this work have furthered our understanding of the principles underlying the long-term stability of neuronal network function.